In a statement, Rendell calls Specter "a mentor, colleague and a political institution."
On a personal level, he said, Specter was "my first boss." Rendell served as an assistant prosecutor when Specter was Philadelphia's district attorney.
Rendell also called Specter "a champion for veterans across our state and beyond" and said he "will be deeply missed."
Specter's son, Shanin, says his father died Sunday at his Philadelphia home from complications of non-Hodgkin lymphoma. He was 82.